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How do you solve this equation: -2m+3=|15+m|

User Trivikram
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1 Answer

5 votes

Any number inside the modulus sign becomes positive. This means
|15+m|=|-(15+m)|=|-15-m| and so we have,


-2m+3=|15+m| \Rightarrow \left \Big\{ {{-2m+3=15+m} \atop{-2m+3=-15-m}} \right

Solving these gives us


-2m+3=15+m \Rightarrow m=-4


-2m+3=-15-m \Rightarrow = m=18

However if we check the second solution in the original equation we obtain
-2(18)+3=|15+18| \Rightarrow -33=33. This is false and so
m=18 can't be a solution.

Therefore the only solution is
m=-4.

(Note: I'm not sure why the second solution didn't work but when there's a modulus sign involved it always pays to check your final answers to be sure. I'll have a think about it but in case you find out before I do, I'd be interested to know in the comments.)

User Markus Kull
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